If f is continuous and ∫ (0 to 81) f(x) dx = 14, find ∫ (0 to 9) xf(x^2) dx
If f is continuous and ∫ (0 to 81) f(x) dx = 14, find ∫ (0 to 9) xf(x^2) dx
find the coordinates of all points where the curve of x2-xy+y2=1 has vertical tangents.
find the inflection point,or points, if any, on the graph of f(x)=(x+2)(3/5)-1
Given (x-y)+sec2(x+y)=tan2(x+y)+(x+y), find dy/dx in simplest form.
If F(x) and g(x) are differentiable functions and F(3)=5 F'(3)=-7 g(3)=-1 g'(3)=4, find the derivative of fg at x=3
The line tangent to the graph of f at the point (k,f(x)) intercepts the x-axis at x=4. What is the value of K if f(x)=12-x^2 for x is greater than or equal to 0 and f(x) is greater than or equal to...
Estimate the area under the curve f(x) = x2 from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer.
List x1, x2, x3, x4 where xi is the right endpoint of the four equal intervals used to estimate the area under the curve of f(x) between x = 3 and x = 5. 3, 3.5, 4, 4.5 3, 3.2, 4.6, 5...
1. How long will it take $5,000 to compound continuously to $30,000 at 8% interest? Choose the closest answer. 2. Find all points 0 < c < 2 where f (2) -f (0) =f '(c)(2 -0), for...
If F(x) = f(xf(xf(x))), where f(1) = 5, f(5) = 6, f '(1) = 3, f '(5) = 4, and f '(6) = 5, find F '(1).
f(x) = (x2 − 4)/(x − 2) if x < 2 ax2 − bx + 3 if 2 ≤ x < 3 2x...
10^x+5^x+1
8/(1 + x2) #39, p395
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 60t at which time the fuel is exhausted and it becomes a freely "falling" body...
Find equations of both the tangent lines to the ellipse x^2 + 9y^2 = 81 that pass through the point (27, 3).
Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for...
Let r=6x5/4,x>0. Use differentials to estimate the percentage change in r, if x increases by 4 . What is the percentage change in r?
Find the critical numbers of the function : h(t) = t3/4 - 2t1/4 I know I first need to find the derivative: 3/4 t-1/4 - 1/2 t-3/4 I know I need to...
A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s2. Its maximum cruising speed is 90 mi/h. (a) What is the maximum distance the train can travel if it accelerates...
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim(x-->1) (x^(9a) - 9ax + 9a - 1) / (x-1)^2